Geodesic
Elementary abelian regular coverings of Platonic maps
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 461-491.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We classify those orientably regular maps which are elementary abelian regular branched coverings of Platonic maps $\mathcal M$, in the case where the covering group and the rotation group $G$ of $\mathcal M$ have coprime orders. The method involves studying the representations of $G$ on certain homology groups of the sphere, punctured at the branch-points. We give a complete classification for branching over faces (or, dually, vertices) of $\mathcal M$, and we outline how the method extends to other branching patterns.
Classification : 05C62, 05C10, 20B25, 05C70
Keywords: orientably regular map, Platonic map, elementary abelian covering, automorphism group 
@article{JAC_2015__41_2_a3,
     author = {Jones, Gareth A.},
     title = {Elementary abelian regular coverings of {Platonic} maps},
     journal = {Journal of Algebraic Combinatorics},
     pages = {461--491},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__41_2_a3/}
}
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Jones, Gareth A. Elementary abelian regular coverings of Platonic maps. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 461-491. http://geodesic.mathdoc.fr/item/JAC_2015__41_2_a3/